Data-driven analysis of the local current distributions of 316L stainless steel corrosion in NaCl solution

doi:10.21203/rs.3.rs-2109820/v1

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Data-driven analysis of the local current distributions of 316L stainless steel corrosion in NaCl solution

https://doi.org/10.21203/rs.3.rs-2109820/v1

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This investigation proposes using Scanning Electrochemical Cell Microscopy (SECCM) as a high throughput tool to collect corrosion activity datasets from randomly probed locations on electropolished 316L SS. In the presence of chloride (varying concentrations), potentiodynamic polarisation tests (varied scan rates) triggered the development of pitting corrosion. Data science methods were deployed to handle, explore, and store the 955 j Vs E curves (public datasets). Normality tests and fitting with theoretical functions were used to understand the conditional log(j) distributions at different potentials. Unimodal and uniform distributions were assigned to the passive and pitting regions. Our local strategy aligned with “big-data” analysis revealed a potential-dependent distribution of log(j), with the amount of randomness increasing with the testing aggressiveness.

Humankind has developed a metals-based civilisation by taking advantage of the stable surface properties of passive metals/alloys, including stainless steels (SS)¹. While the passive film dramatically reduces the rate of generalised corrosion, catastrophic failure remains possible, as passivity comes with various potential forms of localised corrosion. Aggressive species such as Cl⁻, in combination with surface heterogeneities, trigger the breakdown of the passive film, allowing the development of pitting corrosion².

As pitting events are relatively rare and unpredictable, pit initiation has often been considered stochastic in the literature^3–6. This unpredictability is accounted even for traditional alloys: recent data-driven surveys found that the effect of Cr, traditionally correlated to enhanced passivity, is dynamic rather than static, intensifying localised corrosion of weathering steels in the long-term⁷. From a macroscopic perspective, describing the pitting process as events occurring randomly in time and space has seemed straightforward^3,5,6,8.

Nevertheless, multiarray electrode approaches have suggested pit generation to deviate from stochastic behaviour^3,9−11. Shibata and Takeyama, in their work “Stochastic theory of pitting corrosion”, showed that a large ensemble of pitting potential values of 304 SS follows a normal distribution^5,11. Using a 5x5 array of 25 electrodes consisting of closely spaced 316 SS wires, Lunt et al. considered a combination of stochastic (initiation) and deterministic (memory factor, such as surface damage) effects in the pit pattern formation under potentiostatic control. In parts I and II of “Cooperative Stochastic Behavior in Localized Corrosion”^9,10, the authors showed a correlation of current spikes with metastable pits on prior events on 316 SS. Metastable pitting data at low Cl⁻ solution concentrations approached a random distribution of the event times, while metastable pitting no longer occurred randomly at higher concentrations (bursts of coupled events)^9,10.

In all cases, the complete spatiotemporal prediction of localised corrosion is not possible to date^3,5. Existing deterministic models for predicting pitting growth^12,13 are only reliable for upcoming critical (and more easily detectable) events. Models based on atomic-scale descriptors (Point Defect Model) can estimate the nucleation rate of metastable/stable pits^1,12 and the sites most prone to corrosion initiation but are complex and time-consuming. Finite Element Modelling approaches are reliable only if all input variables/boundary conditions are well known, being rarely the case in practice¹⁴. As pitting corrosion is sensitive to slight specimen-to-specimen variability^5,15, deterministic modelling (linking specific outputs with specific inputs) is hardly transposable to slightly different scenarios.

The conclusion from extensive data analysis is that a reliable prediction of localised corrosion could only be made in probabilistic terms^13,16. Stochastic approaches have been elaborated to handle such high randomness and the large scatter typically observed in pitting potential/induction time^5,12,17. Statistical methods used to simulate local corrosion are often based on the measurement of corrosion depths (including the theory of extreme value analysis, the Frechet extreme value distribution, and Bayesian inference^7,8). However, as accurate measuring of corrosion depths is laborious and hardly automated, the datasets obtained are often specific and limited in size. The ideal predictive modelling tool for pitting would rely on the early detection of localised corrosion^18–20.

Spatially resolved electrochemistry^21,22 has been extensively applied to identifying the driving force of localised corrosion. However, typically, relatively small datasets acquired by local electrochemical techniques are reported. On the other hand, macro electrochemical methods provide datasets describing the overall response but provide models that neglect local behaviours that ultimately drive the leading corrosion activities. Seeking to overcome the limitations of local/global electrochemical approaches typically applied to corrosion, this work proposes using a high throughput local tool able to scan a macro surface with repetitive corrosion experiments: the Scanning Electrochemical Cell Microscopy (SECCM).

SECCM has only very recently been employed in corrosion studies^23–30. The method allows electrochemical measurements in a localised Region of Interest (RoI) by confining the electrochemical cell to the meniscus formed between a sharp pipette and a conducting substrate^31,32 and conduct experiments in a large array of independent positions, semi-automatically, which are then used to build spatially-resolved “maps” of electrochemical features. The cell dimensions (micro-capillary pipette size) can range between tens of microns to tens of nm³³. The versatility of the technique in terms of setup and polarisation modes (potentio/galvanostatic, potentiodynamic) has allowed studying a wide range of interfacial phenomena such as (photo)electrocatalysis^34–36, electrodissolution^37–40, electrodeposition^40,41, other phase formation processes⁴², gas evolution reactions⁴³, solid-electrolyte interphases⁴⁴, and nanoimpact electrochemistry³⁸ from a different perspective, including a statistical and probabilistic approach^38,40,41.

On the other hand, only a limited amount of works in corrosion have made use of Machine Learning (ML) approaches^45–59 so far, and the major reasons for their limited application are: 1. the community traditionally relies on low-throughput means for data generation, focusing on specific input-output relationships; 2. the lack of high-quality and public available corrosion datasets readily accessible by computational tools^45,60. This work is an effort in these directions, reporting on a high-throughput local electrochemical technique capable of gathering corrosion “big data” as well as providing structured and downloadable experimental datasets enabling future ML modelling.

In particular, this investigation dissects the current density (j) distributions of 316L SS upon anodic potentiodynamic polarisation, from the active region up to the breakdown potential. Fitting of the distributions with theoretical functions was conducted for the 955 log(j) Vs E curves. Considering the universality of Gaussian distribution in the natural world⁶¹, the normal distribution was first attempted, and results are reported in the form of normality tests. In general, alternative unimodal functions provided the best fit scores at potential regions prior to the passivity breakdown, while uniform distributions were assigned to potential regions related to stable pitting. The testing aggressiveness (Cl⁻ concentration and scan rate pairs) was determinant for the transition between the unimodal and the stochastic behaviour. Our strategy (data-driven high throughput local investigation) is expected to go beyond the corrosion community, as it could be easily replicated in other fields in electrochemistry.

Conditional log(j) distributions as a function of potential

Figure 1 displays one representative potentiodynamic polarisation (j Vs E) curve per experimental combination of [NaCl] and scan rate. First, as expected, the corrosion activity globally increased with chloride concentration. It is well known that the higher the [Cl], the higher the corrosion activity, while the slower the scan rate, the more time is given to Cl⁻ to diffuse to the surface, initiating and propagating localised corrosion^2,5,11. In a recent deep learning framework for uncovering compositional and environmental contributions to pitting resistance, chloride was found to be universally detrimental for passivating alloys⁶².

Noticeably, the magnitude of the j values recorded (~ 5x10²-1x10³ µA/cm²) were not comparable to those found for 316L in chloride media during the macro polarisation^63,64, where the reported values were typically ~ 10³-10⁴ orders of magnitude lower. Despite the sparse literature on SECCM applied to corrosion, a few selected papers converted the corrosion I measured with the meniscus-cell to current density^27,65. The following j ranges (µA/cm²) were reported for pure Al⁶⁵, pure Mg⁶⁵ and polycristalline zinc²⁷ during potentiondynamic polarisation: ~1x10²-1x10³, ~5x10³-5x10⁴ and ~ 1x10⁶-1x10⁷. Thus, the j values here measured for 316L SS were comparable to those determined for pure Al, which is also considered a passive metal. Gateman et al. ⁶⁵ observed that the absolute values of corrosion j obtained with she SECCM were much higher than the ones found with classical polarisation. This may be due to the fast scan rates employed⁶⁶ and/or the effect of miniaturising the electrochemical cell⁶⁷, where the concentration of reducing species within the electrolyte increases due to the change in the diffusion field’s geometry, thus increasing the anodic corrosion reaction rate.

To infer the complete distribution of the current density based on hundreds of curves, the frequency of log(j) as a function of applied anodic potential is presented in Fig. 2 for all datasets. In other words, each 3D plot in Fig. 2 offers the frequency histogram (%) of the conditional log(j) for each E interval, thus serving as probability surface maps.

These surface plots were coloured according to the rainbow spectrum, from violet to red (lower to higher overpolarisation regions, respectively). As the warmer the colour the higher the applied E, higher current density values tend to appear in red/orange/yellow in this representation. The mode value(s) of the conditional log(j) at each potential are highlighted by black markers.

At E ≈ 0.5 V, it could be seen that the log(j) distributions were approximately unimodal (mode at ~ 1x10² µA/cm²), regardless of the testing aggressiveness. These well-defined regions (highest frequencies among all surface plots) corresponded to the active (pre-passive) region. The distribution was more platykurtic (negative excess kurtosis) in 0.005 M NaCl (a) than in 0.01 M NaCl (b, c), which presented a positive skewness. In 0.05 M NaCl (d, e), the distributions were even more positively skewed, suggesting that higher [Cl] induced more positive log(j) values already at 0.5 V.

The medium overpolarisation regions (represented by the blue/green points in the 3D plots) correspond to the passivity domain (a region where the current density is independent of the applied potential²). In these E ranges, the conditional mode values of log(j) presented the least dispersion (j_pass). Although these distributions were generally unimodal, increasing the testing aggressiveness (from a to e) leveraged the probability of collective outliers larger than j_pass. This positive shift in the current resulted from pitting corrosion events, as expected within the passivity domain of 316L in chloride-containing media.

In the higher overpolarisation regions (yellow/orange/red colours), a sudden increase in current density was generally depicted, characterising the passivity breakdown (stable pitting formation)². Simultaneously, the log(j) distributions became more right-tailed, tending to pass from unimodal to multimodal-like (number of black markers higher than 1) as a function of E. Both trends were more easily recognised as the testing aggressiveness increased (from a to e). For instance, at 0.05 M NaCl − 50 mV/s, the data spread towards higher log(j) occurred at similar frequencies (apparent uniform distribution).

Normality tests

At potential values lower than the passivity breakdown, the conditional log(j) distributions were generally unimodal, but could normal distributions describe these data samples? Statistical normality tests for quantifying deviations from normality were deployed for this purpose.

The Anderson-Darling test was applied to the log(j) distributions at each surveyed potential. The results obtained from a surface plot mainly comprising unimodal distributions (0.005 M NaCl, Fig. 2 - a) are presented in Fig. 3. The normality plots of the other surface plots are accessible in the Supplementary Information (Fig. S1). As shown in Fig. 3, for a low significance level (α = 0.05), the test statistic values (grey dots) were systematically higher than the calculated critical value. Therefore, one concluded that the conditional log(j) could not be considered as normally distributed in the considered feature space (different combinations of scan rate/applied potential during potentiodynamic polarisation, and [Cl⁻]). Noticeably for 0.005 M NaCl, the distance from normality was relatively smaller in the pre-passive and passive regimes and progressively higher when entering the stable pitting domain. Although for a few sparse potentials, the null hypothesis was occasionally rejected (normal distributions observed in Fig. S1 c and d), the same overall conclusion held for all experimental configurations: the conditional log(j) was decisively not normally distributed.

Fitting with theoretical functions

The conditional log(j) values were not normally distributed, but would other theoretical functions fit the data with high precision? In this quest, we resorted to distfit, a python package that allows for probability density fitting across 89 univariate distributions by the residual sum of squares (RSS) (distfit scores each of the different distributions for the fit with the empirical distribution and return the best scoring distribution)⁶⁸. Figure 4 illustrates the approach to finding the best fitting function and corresponding RSS for the different E values (0.05 M NaCl, 100 mV/s). As the RSS is an absolute error measure, a “normalised” version of the metric (log(j) values normalised between 0 and 1) was preferred to account for the different data intervals as a function of E. In Fig. 4b - g, for illustrative purposes, the actual log(j) values (instead of the normalised values used in the RSS calculation) are presented. An identical approach was applied to all datasets, and resulting plots can be seen in Fig. S2.

As presented in Fig. 4 - a, various theoretical functions (left-y axis) yielded the best-fit score across the independent variable space, all with relatively low errors (right-y axis). As much as for the other datasets (Fig. S2), as a general rule, the obtained RSS values presented local maxima either at low or high potential regions and were relatively steady at potentials related to the passive regions. At lower potential regions, the RSS generally increased with the testing aggressiveness, likely reflective of higher (and more diverse) activities prior to the passive regimes. Moreover, the normal distribution did not appear among all best-fitting functions, while the uniform distribution frequently appeared at high overpotentials.

At high potential regions, the RSS rose sharply (compared to the RSS baseline representing the passive regions) in the two least aggressive conditions only. In the three more aggressive conditions, instead of monotonically increasing, there was a baseline shift/curve discontinuity marking the onset of a new regime (uniform distribution fitting the data at higher potentials).

The uniform distribution presents higher randomness than the deployed unimodal distributions according to the variance criterion (for finite supports, which refers to the range of values a distribution can achieve). The conditional log(j) distribution described by the uniform function in regions most likely related to pitting would account for the high unpredictability of pitting corrosion.

The correlation between the uniform distributions and higher potentials can be inferred from Fig. S3, where the RSS of the fitted curves (from all datasets) are plotted together. The uniform distribution was the best fitting function (red markers) at high potentials in 0.01 M NaCl (50 mV/s) and high/middle potentials in 0.05 M NaCl (100 and 50 mV/s).

Regardless of the dataset, two types of parametric distributions appeared as the best fitting function: unimodal and uniform. In Fig. 4 (from b to g), histograms of log(j) fitted by the selected functions are shown for representative potentials. Again, while the conditional log(j) distributions were unimodal at low and medium potentials (Fig. 4, b - e), they were reasonably uniform at high potentials (Fig. 4, f) at 0.05 M NaCl − 100 mV/s. The same trend could be observed for the other highly aggressive conditions (Fig. 6c and e), as opposed to the least aggressive ones (Fig. 6a and b). Figure 6 presents histograms of log(j) at fixed and extreme (low and high) potentials for all datasets (all in the same frequency and log(j) scales).

Figure S4 groups the outputted RSS when attempting data fitting with the uniform function in the entire E range for all datasets. It can be observed that the fitting errors were inversely correlated with potential, with acceptable RSS at high potentials only. At low/medium potentials, the unimodal type of distribution generally yielded the lowest fitting errors (function names in Figs. 4 – a and S2).

With potential, the frequency of log(j) values exceeding the mode increased, and the distributions gradually became more platykurtic and more positively skewed (Fig. 4, b - g). Overall, the ranges of conditional log(j) distribution considerably expanded with potential. This heteroscedasticity as a function of E was quantified by the conditional variance of (experimental) log(j) (Fig. 5). Another reason for computing the variance was that it is a measure of randomness or uncertainty. Noticeably, the data variance generally boosted with the testing aggressiveness, and this trend could also be visualised for the modelled data (Fig. 7, from a to e).

The fitted log(j) distributions of Fig. 7 are the probability surface maps of Fig. 2 modelled according to the best fitting functions (Figs. 4 – a and S2). In each 3D plot, unimodal curves were given the same colour, while uniform distributions were coloured red.

As observed in the experimental curves (Figs. 1 and 2), the current densities generally increased until reaching passivity, where relative stability preceded the passivity breakdown (Fig. 7). The exception being at 0.05 M NaCl − 50 mV/s (Fig. 7 - e), where passivity was hardly met; as indicated by the mode values (black markers) monotonically higher across the E range.

In terms of data dispersion, the distributions remained relatively constant for 0.005 and 0.01 M NaCl (both at 100 mV/s) while in passive condition (Figs. 7a, b). At high potential regions, however, while the mode of log(j) linearly increased as a function of E in 0.005 M NaCl, it presented a considerable fluctuation in 0.01 M NaCl (100 mV/s). The nonlinearity of the mode observed at high potentials for the latter was illustrative of the diversity of the current distribution when pitting was likely (justifying the implementation of various functions for proper fitting). Such data distribution complexity of 0.01 M NaCl (100 mV/s) can be further appraised in the 2D modelled surfaces (Fig. S5) (not all data points can be visualised in the 3D representations of Fig. 7).

Concerning the more aggressive conditions (Figs. 7 - c, d, e), the log(j) dispersion progressively raised from the pre-passive to the pitting regions (following the variance plot (Fig. 5)). In these cases, the considerably high data scatter at higher potentials, characterised by multimodal/amodal distributions, justifies the conditional log(j) described by uniform distributions (red curves).

In summary, the higher the corrosiveness, the higher the data dispersion (conditional variance), and the more likely the conditional log(j) was uniformly distributed at high potentials. Figure 6 indicates this trend of log(j) (typically presenting a unimodal distribution, such as at 0.5 V) potentially reaching a stochastic regime (characterised by the uniform distribution), such as at 1.35 V.

Populations of experimental curves: local interpretation

Figures 8 to 12 show the entire population of the experimental curves for each CPP testing configuration. Inspired by Individual Conditional Expectation (ICE) plots (by displaying one line per instance that shows how the instance’s prediction changes when a feature changes, ICE plots aim at representing many curves that are often difficult to appreciate⁶⁹), each j Vs E curve was coloured according to the distance between the sample and the conditional population mean (rainbow colourmap linearly spaced for j). Grey vertical lines were traced at potentials where the uniform function produced the best fit for the conditional log(j) distribution (Figs. 10, 11 and 12). It could be seen that the mean curves were not of much value for describing entire datasets, especially in the cases where both types of distribution (unimodal and uniform) were present.

These experimental curves confirmed that the considerable data scattering observed at increased potentials was strongly caused by pitting corrosion events. One could follow the increased complexity in the j distributions (accompanied by the increased conditional variances, Fig. 5) with the testing aggressiveness. In particular, the discontinuous profile of the conditional log(j) distributions observed for 0.01 M NaCl (100 Mv/s) at high potentials (Figs. 7 – b and S5) could be attributed to current spikes (pitting) from individual j Vs E curves, as shown in Fig. 9. The diversity in terms of current spike profiles was most likely related to pits differing in size, number, location (concerning the heterogeneous sample surface) and position (concerning the droplet-confined region).

One can see that when the conditional log(j) was uniformly distributed at high potentials (Figs. 10 and 11), nearly the entire data population had reached stable pitting. However, in less aggressive conditions (Figs. 8 and 9), although the totality of curves also eventually reached stable pitting (at E = ~ 1.25 V), the log(j) values were never considered uniformly distributed.

The local interpretation of curves suggested that stable pitting solely was not sufficient for triggering the stochastic behaviour of log(j). From a global interpretation perspective (Fig. 5), a “conditional variance threshold” would also be necessary for the log(j) distribution having high randomness. One can observe that the variance values for 0.01 M NaCl (50 mV/s) and 0.05 M NaCl (100 mV/s) were significantly larger than for 0.005 M NaCl and 0.01 M NaCl (100 mV/s) at the stable pitting region. Specifically, it seemed that a conditional variance of log(j) higher than 9 would thus be correlated with the stochastic behaviour.

An exception to this “variance threshold” would be the most aggressive condition case (0.05 M NaCl, 50 mV/s), in which the uniform distribution kicked in at much lower potentials (Fig. 12). In there, not only the highly random behaviour occurred with variance values significantly lower than 9 (Fig. 5), but only a minority of the curves population displayed stable pitting behaviour at the concerned potentials.

The three data clusters distinguishable in Fig. 12 might explain the overall stochastic behaviour of this dataset. These three groups were defined by: passive-like behaviour regardless of the E, stable pitting for E > ~ 1.15 V and stable pitting at much lower potentials (starting from E = 0.5 V). The origin of this three-clustered behaviour is unknown to date and will be addressed in the future with approaches for identical location correlation of SECCM footprints with surface analysis. As the 316L sample surface was randomly probed multiple times, the differences observed among the datasets were considered significantly different. In other words, particular surface features (grains, grain boundaries, inclusions, etc^2,5), determining the three-fold behaviour observed at 0.05 M NaCl (50 Mv/s), had the same likelihood of being scanned regardless of the testing configuration. Therefore, a probable explanation would be that particular surface features would be more or less active depending on the experiment’s corrosiveness. Higher testing aggressiveness would trigger more diverse (higher variance) electrochemical responses, and the outcomes of Fig. 12 would be an extreme case in this sense. Corroborating this hypothesis, careful inspection of the following most aggressive tests revealed additional behaviour clusters similar to the extreme case (Fig. 12): stable pitting at much lower potentials (Figs. 10 and 11); and the few curves remaining passive-like throughout the E range (Fig. 11). On the contrary, in the least aggressive conditions (Figs. 8 and 9), only one cluster of behaviour typical of the 316L polarisation was observed, implying that the electrochemical responses were overall lesser sensitive to local surface variabilities.

In conclusion, the more aggressive the testing condition, the higher: 1. the conditional variance (a measure of randomness) of the log(j) distributions – in general, and especially in the stable pitting region); 2. The likelihood of uniform distribution (high randomness) related to stable pitting behaviour (combination of [Cl⁻] and scan rate at least as aggressive as 0.01 M and 50 Mv/s, respectively); 3. The conditional variance of the uniform distribution.

Material

The investigated stainless steel consisted of an industrial plate of 316L (Aperam, France) subjected to electropolishing (bath temperature = 65°C, current densities between 20 and 40 A/dm²) followed by passivation (Packo Inox, Belgium)⁶⁴. For SECCM testing, one squared coupon (~ 1 cm²) was cut with a lever cutter and degreased in acetone (10 min in ultrasonic bath).

SECCM experiments

1254 Cyclic Potentiodynamic Polarisation (CPP) tests were carried out on the same 316L sample using the SECCM platform in hopping-mode protocol. In brief, the SECCM probe was brought into contact with the surface at randomly selected locations, and upon each landing 1 Cyclic Voltammogram was recorded. The probe retracted and moved to a new location automatically to acquire the corrosion data. Five different combinations of [NaCl] and voltammetric scan rates were employed: 0.005 M NaCl – 100 Mv/s, 0.01 M NaCl – 100 Mv/s, 0.01 M NaCl – 50 Mv/s, 0.05 M NaCl – 100 Mv/s, 0.05 M NaCl – 50 Mv/s. A total of 12 SECCM sessions were performed, comprising maps with up to 17x17 points (during up to 24 h of continuous measurement).

Worthy mentioning that the scan rates for corrosion studies with the SECCM can be much higher than those used in conventional macroscale corrosion tests due to the enhanced mass transport inside the meniscus^66,70,71. Despite Shkirskiy et al. finding that ORR favoured the SECCM meniscus spreading during the corrosion of zinc²⁷, our preliminary SEM-FEG analysis of SECCM footprints suggested significant droplet stability.

Single-barrel pipets (borosilicate) were pulled with a Sutter P2000 pipet puller to a final internal circular diameter of ~ 2 µm, and were used as SECCM probes. The droplet size is expected to be of similar dimensions as the probe, and this was confirmed with preliminary FE-SEM images of the SECCM footprints on the SS surface. Current density j was then calculated by normalising the measured current by 3.14 µm², assuming a consistent droplet size. Ag/AgCl quasi reference counter electrodes (QRCEs), well known for their long-term stability⁷², were inserted into pipets filled with the NaCl electrolyte. The sample time was 30 µs, time constant was 100 µs, with 256 number of samples per data point. The starting E was − 0.5 V, and the end anodic E was 1.355 V. OCP values varying roughly between 0 and 200 mV Vs Ag/AgCl were recorded. A custom-built potentiostat featuring current collectors with a sensitivity of 1 nA/V was employed, and the data collection system (PCIe-7856R FPGA card, National Instruments) was controlled by LabVIEW (2019, National Instruments) interface running Warwick’s software (WEC-SPM, www.Warwick.ac.UK/electrochemistry). To avoid any perturbation from sound, light or mechanical vibrations and reduce electrical noise, the experiments were performed inside a faraday cage (Thorlabs) equipped with acoustic insulation panels (Kevothermal) and aluminium heat sinks, mounted on top of an optical table (TMC Ametek) with automatic levelling.

Meniscus instability can result as a part of the hopping-mode protocol when the SECCM meniscus does not wet the surface adequately, producing a phantom contact. In these cases, either discontinuous or extremely low electrochemical signals were recorded, and related curves treated as global outliers were removed from the datasets. In total, 76.2% of the recorded curves were considered actual data samples (true corrosion signals). Initially, one map was obtained per testing configuration, and meaningful data, with sufficient dispersion, was generally obtained for the most aggressive testing conditions. Next, more SECCM measurements were conducted, especially for the least aggressive configurations displaying less data dispersion. In these latter cases, although the initial data distributions barely changed upon further testing, the final datasets comprised samples from all maps. The final quantities of selected j Vs E curves were: 287 (0.005 M NaCl – 100 mV/s), 377 (0.01 M NaCl – 100 mV/s), 119 (0.01 M NaCl – 50 mV/s), 125 (0.05 M NaCl – 100 mV/s) and 47 (0.05 M NaCl – 50 mV/s). All 955 polarisation curves are accessible at Mendeley data.

Data analysis

The code for data processing and visualisation was written in Python 3.7 language and has been made available at GitHub (as Jupyter Notebook files).

For normality checking (Anderson-Darling test), the scipy.stats package was used (anderson function). If the returned test statistic is larger than a critical value corresponding to a chosen significance level, the null hypothesis that the data come from a normal distribution can be rejected.

Fitting with theoretical functions was executed using the distfit package comprising 89 univariate distributions (stats.scipy library)⁶⁸. Implementation of distfit returns the theoretical distribution with the best goodness of fit (based on the Residual Sum of Squares) and associated RSS values. The RSS describes the deviation predicted from actual empirical data values (the differences in the estimates), being a measure of the discrepancy between the data and an estimation model. The RSS was computed according to Eq. 1, where y_i is the i^th value of the variable to be predicted (normalised log(j)) and ŷ_i is the value returned by the estimated density function. For the “normalised” error metric (log(j) values converted to the [0,1] interval), the minmax_scale function of the sklearn.preprocessing library was chosen.

\(RSS=\sum _{i=1}^{n}{({y}_{i}-{\widehat{y}}_{i})}^{2}\) (Eq. 1)

For general data processing, analysis and plotting, the Numpy, pandas and Matplotlib libraries were employed⁷³. The statistics function from the sub-package scipy.stats was used for calculating the variance⁷⁴.

j Vs E datasets

The datasets considered here were sliced from 0.5 V (considerably higher than the OCP) upward to avoid the eventual and deleterious occurrence of negative currents. Positive j values were preconised for building histograms (Fig. 2) and for obtaining defined numbers of log(j), whose conditional distribution was the scope of this work.

The SECCM experiments were designed to detect low corrosion currents, and the trade-off for such a high signal sensitivity was the I saturation level at 10 nA. In case of missing data points in the anodic sweep data (most often caused by oversaturation at high applied overpotentials), these were replaced by data interpolation (pandas interpolate() method, spline). This data filling procedure was used for a small proportion of the data populations (0%, 0%, ~ 1%, ~ 1% and ~ 11%, respectively, for the datasets with increasing testing aggressiveness). The final shapes of the j Vs E curves were validated against similar curves with unsaturated signals at the relevant E ranges. All datasets are available online at Mendeley Data as .csv files.

Data availability

All data generated or analysed during this study are included in this published article (and its supplementary information files) and are available in the Mendeley Data repository, [PERSISTENT WEB LINK TO DATASETS].

Code availability

The code required to reproduce these findings is included in this published article (and its supplementary information files) and is available to download from GitHub: https://github.com/bcoelho-leonardo/Data-driven-analysis-of-the-local-current-distributions-of-316L-corrosion-in-NaCl-solution/blob/72b197178fe04cc7bd41d34dac19893835492c7d/Data-driven%20analysis%20of%20the%20local%20current%20distributions%20of%20316L%20stainless%20steel%20corrosion%20in%20NaCl%20solution_code.ipynb.

AUTHOR CONTRIBUTIONS

L.B.C.: Conceptualisation, Methodology, Software, Formal analysis, Data Curation, Writing - Original Draft, Visualization, Project administration, Funding acquisition. D.T.: Validation, Investigation, Writing - Review & Editing, Visualization. M.B.: Investigation, Writing - Review & Editing. G.P.: Software. G.B.: Validation, Formal analysis, Writing - Review & Editing, Visualization. J.U.: Validation, Formal analysis, Resources, Writing - Review & Editing, Visualization, Supervision.

Acknowledgements

The author L.B. Coelho is a Postdoctoral Researcher of the Fonds de la Recherche Scientifique – FNRS (Belgium) which is gratefully acknowledged. D.T. acknowledges financial support to the Fonds de Recherche dans l’Industrie et dans l’Agriculture (FRIA). J.U. and M.B. acknowledge financial support to the Fonds de la Recherche Scientifique de Belgique (F.R.S.-FNRS) under Grant No. F.4531.19 and to the Fonds Wetenschappelijk Onderzoek (FWO) under contract G0C3121N. G.B. and G.P. are supported by the Service Public de Wallonie Recherche under grant nr 2010235–ARIAC by DigitalWallonia4.ai. The authors acknowledge Prof. Marjorie Olivier (University of Mons) for providing stainless steel treated plates. The author L.B. Coelho would like to thank Dr. Denis Steckelmacher for fruitful discussions on data manipulation and analysis.

Additional Information

Competing interests: the authors declare no Competing Financial or Non-Financial Interests.

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jVsEdatasets.7z
Data Set 1
Datadrivenanalysisofthelocalcurrentdistributionsof316LstainlesssteelcorrosioninNaClsolutioncode.unk
Data Set 2
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Data-driven analysis of the local current distributions of 316L stainless steel corrosion in NaCl solution

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